“The No. 1 thing Republicans could do to mess that up is to refuse to stand for principle,” Cruz said. “And if the House turns around and passes a giant amnesty deal that doesn’t secure the border and grants amnesty, I think they might as well go and put 'Harry Reid for majority leader' bumper stickers on the backs of their cars because it would be kicking conservatives, kicking the tea party, kicking millions of Americans in the teeth to make that same mistake again and so I sure hope they don’t do it.”

But lawmakers in the House want to achieve immigration reform, preferably early next year, by passing a comprehensive bill like the Senate did. Moreover, House Speaker John Boehner, R-Ohio, recently made a shocking but telling move regarding restructuring the broken system. He hired Rebecca Tallent, who was director of immigration policy at the Bipartisan Policy Center, to head his reform team -- a move that conservatives oppose, as they consider Tallent to be too pro-immigration.

And Reid, a Democrat from Nevada, believes Boehner will eventually cave and conference the House and Senate bills. That’s despite the speaker having said he has no intention of doing so.

“Why wouldn’t he? He’ll have a lot of pressure from his members now that the election is getting closer,” Reid told The Hill. “Some of his members are in very marginal districts, where they need to do something on immigration.”

The Senate bill is more than 1,000 pages of legislation that includes improvements to border security and a 13-year pathway to citizenship. Conservatives oppose the idea of citizenship, arguing it is similar to amnesty for immigrants who broke the law to remain in the country illegally.